There's actually SO much to do in Edmonton and lots of hidden places, but I think 3-4 days would be enough to check out a few that sound most interesting to you. Here is a list of recommendations to get you started:

FOOD

•  The Commodore on Jasper Ave - cheap cash-only breakfast diner
•  Farmer's Markets - there are lots of outdoor markets all over the city, including Old Strathcona off Whyte Ave, Dowtown City Market on 104 Street, and 124 Street Grand Market . Good for people watching as well as food.
•  Food trucks in Churchill Square downtown
•  Native Delights - Aboriginal cuisine on 118 Avenue
•  Pho - there are lots of great Pho places in town, it's kind of a staple
•  Earth's General Store - organic and local grocer, including personal care items, book collection, and more... plus their downtown location has a nice deli
•  Dadeos on Whyte - cajun food, sweet decor  
• Burger Baron - excellent burger place, multiple locations all around the city, avoid the 95 St location
•  The Bistro - independent caterers on 118th Ave, check their Facebook to see if they're open on any given week and what their specials are that day (http://goo.gl/KqpB2B)
•  Padmanadi's - excellent veg food that looks & tastes like meat haha, kind of Asian fusion style... highly recommend buffet night if there's one going on
•  Pagolac - Vietnamese in Chinatown
•  Sai Woo Gardens - best Cantonese food in Edmonton
• Veggie Garden - suuuuuper cheap vegetarian vietnamese & chinese food
•  Abyssinia - best Ethiopian food (though most people will probably recommend Langano Skies on Whyte, this place is much cheaper, tastier & WAY faster)
•  Sapporo sushi is pretty good, but if you're gonna make it to the West coast then don't bother with sushi here in the prairies!!
•  Friends & Neighbours - combo of western diner food & Pho

COFFEE / TEA

There are TONS of great coffee shops, but here are a few...

•  The Tea Girl on 124 St & Stony Plain Road
•  Credo - multiple locations, a little on the hipster suits side
•  Remedy - multiple locations, best place for a good Chai
•  Leva - also a hipster haunt! great food & coffee though, near university
•  Duchess Bakery - just got named one of the best bakeries in the world!

THRIFT / SECONDHAND / VINTAGE & ANTIQUE SHOPS

•  Bissell Centre - classic charity thrift shop on 118 Ave & 89 St
•  The Junque Cellar on Whyte Ave - vintage & retro furniture, clothing & decor
•  The Wee Book Inn - there are like four locations around town and they all have a resident rescue cat!
•  Local gifts - curated vintage & handmade goods (http://www.localgifts.ca/)
• Antique Malls - Blue Jar (Stony Plain Rd) & Old Strathcona (off Whyte) especially
•  Find store - furniture, housewares & decor thrifting

OUTDOORS

Edmonton has some of the most amazing outdoor spots. Here are a few:

•  Mill Creek Ravine
•  River Valley - basically anywhere along the river which is the "largest stretch of urban parkland in North America"
•  The End of The World (http://goo.gl/CtZAIu)

PLACES TO CHILL / PEOPLE WATCH

•  Churchill Square downtown - always interesting people watching, plus the public library is across the street, and there are lots of little lunch places and cafes nearby
•  Legislature grounds - beautiful grounds to hang out in on a sunny day, and there are often people chilling with music etc who are happy to chat
•  Gazebo Park & End of Steel Park off Whyte Ave
•  University of Alberta campus - it's worth checking out since there's some neat architecture (highly recommend a walk through Rutherford Library), nice places to sit outside & indoors, and it's on the LRT line so super convenient
•  MacEwan university is a neat urban campus, all indoors - good place to rest up on a rainy day, North end of downtown (104 Ave)

FESTIVALS

There are SO many all summer. Just google and you'll get a huge list... I'm sure there's something going on in May!

ARTS & MOVIES

•  Art Gallery of Alberta - free admission last Thursday of every month from 6-9pm
•  Nina Haggerty Centre for the Arts
•  Latitude 53 - multi-use exhibition space
•  Garneau Theatre for movies
•  Princess Theatre for movies
•  Royal Bison Arts & Crafts Fair is May 8-10 if you're here then (http://royalbison.ca/)

MUSIC

I'm not really into the music scene, but here are some places to start looking:

•  Not Enough Fest (https://www.facebook.com/NotEnoughFest)
•  Venues: The ARTery (closed but hopefully they'll reopen a new location soon!), the New Wunderbar, Bohemia

BEER

Also not a huge thing of mine, but I know there's a major scene here.

•  Google Edmonton brewery district
•  Yellowhead brewery

BARS / DANCING

Again, not my thing personally. I'm only familiar with the queer scene, but here's what I know about that:

•  Evolution - friendly vibe, queer dancing
•  Buddy's - gay bar, less friendly vibe, more electronic
•  Fruit Loop - queer pop up events (https://www.facebook.com/fruitloopedmonton)
•  Empress Ale House - hosts Beers for Queers last Thursday pf every month

INTERESTING NEIGHBOURHOODS

For some of these I recommend going during the day unless you're specifically going out drinking on Whyte or Jasper. 118th, 107th, Stony Plain Rd, Chinatown & Little Italy all have reputations for being rougher areas... I've lived near all and it's not really that bad, but make your own decisions!

•  Whyte Avenue & Old Strathcona, Garneau
•  Jasper Avenue
•  104 Street north of Jasper ave
•  118 Avenue between 101 St & 82 St
•  107 Avenue between 101 St & 82 St
•  Stony Plain Road west of 149 Street
•  124 Street between Jasper and 107 Ave
•  Chinatown & Little Italy - 99 Street & 95 Street

RANDOM

•  Board game cafes if you're into that stuff! There's the "Hex Cafe" and "Table Top" that I know of.
•  Muttart conservatory is sweet and definitely worth checking out
•  Radio stations to check out while you're here: Aboriginal Voices Radio (89.3), CJSR (88.5)
•  The Travelling Tickle Trunk - awesome feminist sex-positive adult toy store
•  Pride Centre of Edmonton if you wanna meet some friendly LGBTQ* folks :) It's also a nice place to chill, has comfy couches & free coffee
•  Edmonton Anarchist Bookfair is May 8-10^th
•  Royal Alberta Museum - also close to a set of stairs that’ll take you down to the river valley for a nice walk